4461:
2777:. An expectation-maximisation algorithm consists of a cycle in which the steps of expectation and maximization are repeatedly performed. In the expectation step, the distribution of the hidden variables is computed according to the current values of the probability parameters, while in the maximisation step, the new values of the parameters are computed. Gradient descent methods compute the gradient of the target function and iteratively modify the parameters moving in the direction of the gradient.
28:
2835:. Logical rules are learned from probabilistic data in the sense that both the examples themselves and their classifications can be probabilistic. The set of rules has to allow one to predict the probability of the examples from their description. In this setting, the parameters (the probability values) are fixed and the structure has to be learned.
516:
2838:
In 2011, Elena
Bellodi and Fabrizio Riguzzi introduced SLIPCASE, which performs a beam search among probabilistic logic programs by iteratively refining probabilistic theories and optimizing the parameters of each theory using expectation-maximisation. Its extension SLIPCOVER, proposed in 2014, uses
2443:
with anti-entailment. However, the operation of anti-entailment is computationally more expensive since it is highly nondeterministic. Therefore, an alternative hypothesis search can be conducted using the inverse subsumption (anti-subsumption) operation instead, which is less non-deterministic than
416:
209:
system introduced by
Muggleton, Dianhuan Lin, Niels Pahlavi and Alireza Tamaddoni-Nezhad in 2014. This allows ILP systems to work with fewer examples, and brought successes in learning string transformation programs, answer set grammars and general algorithms.
674:. Weak consistency is implied by strong consistency; if no negative examples are given, both requirements coincide. Weak consistency is particularly important in the case of noisy data, where completeness and strong consistency cannot be guaranteed.
2843:
to guide the refinement process, thus reducing the number of revisions and exploring the search space more effectively. Moreover, SLIPCOVER separates the search for promising clauses from that of the theory: the space of clauses is explored with a
204:
Recently, classical tasks from automated programming have moved back into focus, as the introduction of meta-interpretative learning makes predicate invention and learning recursive programs more feasible. This technique was pioneered with the
2812:
programs, where theory compression refers to a process of removing as many clauses as possible from the theory in order to maximize the probability of a given set of positive and negative examples. No new clause can be added to the theory.
126:
introduced several ideas that would shape the field in his new approach of model inference, an algorithm employing refinement and backtracing to search for a complete axiomatisation of given examples. His first implementation was the
2447:
Questions of completeness of a hypothesis search procedure of specific inductive logic programming system arise. For example, the Progol hypothesis search procedure based on the inverse entailment inference rule is not complete by
1679:
sharing the same predicate symbol and negated/unnegated status. Then, the least general generalisation is obtained as the disjunction of the least general generalisations of the individual selections, which can be obtained by
1318:
Bottom-up methods to search the subsumption lattice have been investigated since
Plotkin's first work on formalising induction in clausal logic in 1970. Techniques used include least general generalisation, based on
193:, where by 2000 inductive logic programming had been successfully applied to drug design, carcinogenicity and mutagenicity prediction, and elucidation of the structure and function of proteins. Unlike the focus on
1117:
with respect to these input theories can be found with its hypothesis search procedure. Inductive logic programming systems can be roughly divided into two classes, search-based and meta-interpretative systems.
2340:
4681:
2464:
systems encode the inductive logic programming program as a meta-level logic program which is then solved to obtain an optimal hypothesis. Formalisms used to express the problem specification include
1804:
of a resolution step to compute possible resolving clauses. Two types of inverse resolution operator are in use in inductive logic programming: V-operators and W-operators. A V-operator takes clauses
795:
1691:, which are defined in terms of subsumption relative to a background theory. In general, such relative least general generalisations are not guaranteed to exist; however, if the background theory
901:
511:{\displaystyle {\begin{array}{llll}{\text{Completeness:}}&B\cup H&\models &E^{+}\\{\text{Consistency: }}&B\cup H\cup E^{-}&\not \models &{\textit {false}}\end{array}}}
861:
4587:
2379:
1677:
2256:
and Wray
Buntine in 1988 for use in the inductive logic programming system Cigol. By 1993, this spawned a surge of research into inverse resolution operators and their properties.
636:, but forbids any generation of a hypothesis as long as the positive facts are explainable without it. . "Weak consistency", which states that no contradiction can be derived from
4651:
2437:
2408:
62:(i.e. proving a property for all members of a well-ordered set) induction. Given an encoding of the known background knowledge and a set of examples represented as a logical
1111:
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and the goal is to infer the probabilities annotations of the given clauses, while in the latter the goal is to infer both the structure and the probability parameters of
593:
In
Muggleton's setting of concept learning, "completeness" is referred to as "sufficiency", and "consistency" as "strong consistency". Two further conditions are added: "
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2004:
1977:
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201:. The success of those initial applications and the lack of progress in recovering larger traditional logic programs shaped the focus of the field.
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147:
in 1990, defined as the intersection of machine learning and logic programming. Muggleton and Wray
Buntine introduced predicate invention and
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1320:
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This problem has two variants: parameter learning and structure learning. In the former, one is given the structure (the clauses) of
4061:"Automated identification of features of protein-ligand interactions using Inductive Logic Programming: a hexose binding case study"
3044:
2586:
5195:
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2576:
43:
5055:
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4859:
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4717:
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311:
As of 2022, learning from entailment is by far the most popular setting for inductive logic programming. In this setting, the
5233:
4996:
4626:
3148:. Lecture notes in computer science Lecture notes in artificial intelligence. Berlin Heidelberg: Springer. pp. 354β358.
2926:. Lecture notes in computer science Lecture notes in artificial intelligence. Berlin Heidelberg: Springer. pp. 174β177.
2567:
2452:. On the other hand, Imparo is complete by both anti-entailment procedure and its extended inverse subsumption procedure.
178:, introduced by Muggleton and Feng in 1990, went back to a restricted form of Plotkin's least generalisation algorithm. The
3599:
Muggleton, Stephen (1999). "Inductive Logic
Programming: Issues, Results and the Challenge of Learning Language in Logic".
2761:. Just as in classical inductive logic programming, the examples can be given as examples or as (partial) interpretations.
752:
186:, a descendant of Progol introduced by Ashwin Srinivasan in 2001, is still one of the most widely used systems as of 2022.
5011:
5001:
4779:
2828:
2546:
155:
5395:
5375:
5305:
5248:
5210:
5200:
5160:
5085:
5021:
4991:
4918:
4907:
4804:
4784:
4759:
4722:
4517:
3712:. Lecture notes in computer science Lecture notes in artificial intelligence. Berlin Heidelberg: Springer. p. 197.
3684:. Lecture notes in computer science Lecture notes in artificial intelligence. Berlin Heidelberg: Springer. p. 286.
3659:. Lecture notes in computer science Lecture notes in artificial intelligence. Berlin Heidelberg: Springer. p. 255.
1710:
is itself a clause. In this case, a relative least general generalisation can be computed by disjoining the negation of
1701:
377:
218:
Inductive logic programming has adopted several different learning settings, the most common of which are learning from
2483:, while ASPAL and ILASP are based on an encoding of the inductive logic programming problem in answer set programming.
866:
5350:
5113:
5080:
4975:
4951:
4893:
4789:
4698:
4676:
4661:
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4279:, Lecture Notes in Computer Science, vol. 4455, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 94β108,
3541:
2480:
99:
5297:
5283:
5190:
5150:
5075:
4981:
4961:
4828:
4707:
4641:
3172:
Muggleton, Stephen H.; Feng, Cao (1990). Arikawa, Setsuo; Goto, Shigeki; Ohsuga, Setsuo; Yokomori, Takashi (eds.).
2510:
826:
5390:
5155:
5065:
5045:
5031:
3178:
Algorithmic
Learning Theory, First International Workshop, ALT '90, Tokyo, Japan, October 8β10, 1990, Proceedings
4552:
182:
system, introduced by
Muggleton in 1995, first implemented inverse entailment, and inspired many later systems.
5370:
5330:
5273:
5205:
4943:
4774:
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rules with associated probabilistic uncertainty parameters. Their approach involves generating the underlying
4209:
5380:
5360:
5301:
5288:
5268:
5095:
4832:
4736:
4694:
2866:
2349:
1618:
128:
3063:
Muggleton, S.H.; Buntine, W. (1988). "Machine invention of first-order predicate by inverting resolution".
167:
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59:
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inherent in the early work, these fields used inductive logic programming techniques from a viewpoint of
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5238:
5180:
5132:
4702:
2881:
2876:
2861:
2827:
ProbFOIL, introduced by De Raedt and Ingo Thon in 2010, combined the inductive logic programming system
2805:
2623:
Probabilistic inductive logic programming adapts the setting of inductive logic programming to learning
194:
3818:
5385:
5365:
5325:
5127:
4986:
4855:
4842:
4596:
3348:
2769:
Parameter learning for languages following the distribution semantics has been performed by using an
2413:
2384:
1184:
727:
4026:
3747:
2527:
5320:
5258:
5070:
5050:
5036:
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4631:
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2871:
1786:
1070:
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974:
111:
55:
2801:
2502:
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3491:
3412:
3277:
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1794:
1324:
691:
410:
154:
Several inductive logic programming systems that proved influential appeared in the early 1990s.
148:
2816:
In the same year, Meert, W. et al. introduced a method for learning parameters and structure of
3786:
Proceedings of the 10th international conference on logic programing and nonmonotonic reasoning
2702:
the goal of probabilistic inductive logic programming is to find a probabilistic logic program
5293:
5185:
5040:
5016:
4956:
4923:
4885:
4870:
4809:
4523:
4436:
4380:
4330:
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4253:
4190:
4125:
4092:
4039:
3994:
3886:
3797:
3760:
3713:
3685:
3660:
3511:
3453:
3404:
3383:
Muggleton, Stephen H.; Lin, Dianhuan; Pahlavi, Niels; Tamaddoni-Nezhad, Alireza (2013-05-01).
3364:
3316:
3227:
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3119:
3076:
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2993:
2927:
2790:
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1801:
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234:
144:
47:
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3833:
3789:
3752:
3637:
3608:
3578:
3501:
3443:
3396:
3356:
3308:
3269:
3217:
3109:
3068:
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1122:
2725:
17:
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4666:
4559:
4479:
3860:
2794:
2571:
2531:
2514:
639:
50:
as a uniform representation for examples, background knowledge and hypotheses. The term "
2492:
1239:
1189:
971:
An inductive logic programming system is a program that takes as an input logic theories
940:
910:
800:
732:
703:
4059:
Santos, Jose; Nassif, Houssam; Page, David; Muggleton, Stephen; Sternberg, Mike (2012).
3352:
3300:
3014:
2472:, with existing Prolog systems and answer set solvers used for solving the constraints.
421:
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2144:
2117:
2090:
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2009:
1982:
1955:
1928:
1901:
1854:
1827:
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1719:
1547:
1520:
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1419:
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1365:
1338:
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1259:
1159:
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and learning from interpretations. In both cases, the input is provided in the form of
190:
115:
95:
3612:
3582:
389:
is a set of clauses satisfying the following requirements, where the turnstile symbol
5410:
5263:
4507:
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3416:
2849:
2786:
171:
4448:
4344:
3845:
3281:
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2705:
2594:
1881:
1807:
1598:
1578:
1446:
694:, each of which are themselves a finite set of ground literals. Such a structure
189:
At around the same time, the first practical applications emerged, particularly in
159:
123:
4407:"Structure learning of probabilistic logic programs by searching the clause space"
4364:
4321:, vol. 6489, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 47β58,
4273:"Towards Learning Non-recursive LPADs by Transforming Them into Bayesian Networks"
4272:
3430:
Cropper, Andrew; DumanΔiΔ, Sebastijan; Evans, Richard; Muggleton, Stephen (2022).
2564:
1773:
Relative least general generalisations are the foundation of the bottom-up system
122:
setting around 1970, adopting an approach of generalising from examples. In 1981,
4376:
4284:
4232:
De Raedt, L.; Kersting, K.; Kimmig, A.; Revoredo, K.; Toivonen, H. (March 2008).
4111:
4035:
3867:. Lecture Notes in Computer Science. Vol. 1297. Springer. pp. 296β308.
3793:
3756:
3312:
3173:
5145:
4326:
4121:
3022:
Proceedings of the 7th international joint conference on
Artificial intelligence
2845:
2817:
2604:
2551:
1774:
1687:
To account for background knowledge, inductive logic programming systems employ
183:
175:
136:
119:
4406:
3739:
Proceedings of the 13th international conference on inductive logic programming
3448:
3431:
3384:
3342:
4469:
4432:
4313:
De Raedt, Luc; Thon, Ingo (2011), Frasconi, Paolo; Lisi, Francesca A. (eds.),
4249:
3837:
3400:
3360:
1790:
219:
67:
4533:
4440:
4257:
4194:
4185:
4168:
4077:
3998:
3515:
3457:
3408:
3231:
3123:
4553:
http://john-ahlgren.blogspot.com/2014/03/inductive-reasoning-visualized.html
3536:. In Fayyad, U.M.; Piatetsky-Shapiro, G.; Smith, P.; Uthurusamy, R. (eds.).
2541:
4096:
2824:
equivalent to them and applying techniques for learning Bayesian networks.
2460:
Rather than explicitly searching the hypothesis graph, metainterpretive or
3882:
1571:. The least general generalisation can be computed by first computing all
300:, itself a logical theory that typically consists of one or more clauses.
3989:
3962:
3506:
3479:
3222:
3195:
2984:(Technical report). Department of Computer Science, Yale University. 192.
2507:
63:
1121:
Search-based systems exploit that the space of possible clauses forms a
27:
3273:
3114:
3097:
2832:
2809:
2519:
66:
of facts, an ILP system will derive a hypothesised logic program which
3641:
3058:
3056:
2961:
2840:
2599:
2581:
2465:
179:
132:
4012:
Muggleton, Stephen; Santos, Jose; Tamaddoni-Nezhad, Alireza (2009).
3347:, Cognitive Technologies, Berlin, Heidelberg: Springer, p. 14,
3307:, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 339β364,
2750:
is maximized and the probability of negative examples is minimized.
2612:
1335:
A least general generalisation algorithm takes as input two clauses
3979:
3912:
Learning definite and normal logic programs by induction on failure
3496:
3212:
3065:
Proceedings of the 5th International Conference on Machine Learning
2536:
1067:. A system is complete if and only if for any input logic theories
4423:
4371:, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 61β75,
4218:
3943:
3531:"Inductive Logic Programming and Knowledge Discovery in Databases"
3385:"Meta-interpretive learning: application to grammatical inference"
2797:
in a preliminary step and then applying expectation-maximisation.
2789:
and Avi Pfeffer in 1997, where the authors learn the structure of
2497:
26:
4116:, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 1β27,
3937:
Toth, David (2014). "Imparo is complete by inverse subsumption".
2335:{\displaystyle B\land H\models E\iff B\land \neg E\models \neg H}
1770:
and then computing their least general generalisation as before.
58:(i.e. suggesting a theory to explain observed facts) rather than
4167:
Riguzzi, Fabrizio; Bellodi, Elena; Zese, Riccardo (2014-09-18).
31:
A photo of Family sample for Inductive Logic Programming article
4569:
4547:
Visual example of inducing the grandparenthood relation by the
499:
4475:
A History of Probabilistic Inductive Logic Programming
1310:. This lattice can be traversed either bottom-up or top-down.
4014:"ProGolem: a system based on relative minimal generalization"
303:
The two settings differ in the format of examples presented.
139:
logic programs from positive and negative examples. The term
3915:(PhD). Imperial College London. ethos 560694. Archived from
2722:
such that the probability of positive examples according to
2264:
The ILP systems Progol, Hail and Imparo find a hypothesis
1517:, and that is subsumed by every other clause that subsumes
903:
also holds. The goal is then to output a hypothesis that is
3817:
Yamamoto, Yoshitaka; Inoue, Katsumi; Iwanuma, Koji (2012).
3250:
Muggleton, S.H. (1995). "Inverting entailment and Progol".
2990:
Computational logic : essays in honor of Alan Robinson
2631:
within the formalism of probabilistic logic programming.
4519:
Inductive Logic Programming: Techniques and Applications
4365:"Learning the Structure of Probabilistic Logic Programs"
4169:"A History of Probabilistic Inductive Logic Programming"
3861:"Which hypotheses can be found with inverse entailment?"
3819:"Inverse subsumption for complete explanatory induction"
3782:"Induction on failure: learning connected Horn theories"
3540:. MIT Press. pp. 117β152 See Β§5.2.4. Archived from
2556:
2524:
4018:
International Conference on Inductive Logic Programming
3963:"Inductive Logic Programming At 30: A New Introduction"
3865:
International Conference on Inductive Logic Programming
3480:"Inductive Logic Programming At 30: A New Introduction"
3196:"Inductive Logic Programming At 30: A New Introduction"
551:, and consistency forbids generation of any hypothesis
4478:, Fabrizio Riguzzi, Elena Bellodi and Riccardo Zese,
3904:
3902:
2728:
2708:
2678:
2651:
2638:
background knowledge as a probabilistic logic program
2228:
2201:
2174:
2147:
2120:
2093:
2066:
2039:
2012:
1985:
1958:
1931:
1904:
1884:
1857:
1830:
1810:
1749:
1722:
1601:
1581:
1550:
1523:
1496:
1469:
1449:
1422:
1395:
1368:
1341:
1289:
1262:
1242:
1212:
1192:
1162:
1135:
943:
913:
829:
803:
790:{\textstyle \mathrm {head} \leftarrow \mathrm {body} }
755:
735:
706:
642:
609:
563:
530:
352:
325:
270:
243:
237:), as well as positive and negative examples, denoted
94:
Inductive logic programming is particularly useful in
2493:
1BC and 1BC2: first-order naive Bayesian classifiers:
2416:
2387:
2352:
2290:
1621:
1073:
1027:
977:
869:
419:
395:
3961:
Cropper, Andrew; DumanΔiΔ, Sebastijan (2022-06-15).
3741:. LNCS. Vol. 2835. Springer. pp. 311β328.
3478:
Cropper, Andrew; DumanΔiΔ, Sebastijan (2022-06-15).
3194:
Cropper, Andrew; DumanΔiΔ, Sebastijan (2022-06-15).
2439:, they generalize the negation of the bridge theory
70:
all the positive and none of the negative examples.
5339:
5224:
5126:
4942:
4884:
4841:
4744:
4735:
4675:
4617:
4608:
3788:. LNCS. Vol. 575. Springer. pp. 169β181.
3708:Nienhuys-Cheng, Shan-hwei; Wolf, Ronald de (1997).
3680:Nienhuys-Cheng, Shan-hwei; Wolf, Ronald de (1997).
3655:Nienhuys-Cheng, Shan-hwei; Wolf, Ronald de (1997).
3144:Nienhuys-Cheng, Shan-hwei; Wolf, Ronald de (1997).
2922:Nienhuys-Cheng, Shan-hwei; Wolf, Ronald de (1997).
2565:
Inthelex (INcremental THEory Learner from EXamples)
690:examples are given as a set of complete or partial
4211:Learning probabilities for noisy first-order rules
3301:"Relational Data Mining Applications: An Overview"
2742:
2714:
2691:
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2431:
2402:
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2025:
1998:
1971:
1944:
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1762:
1735:
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1607:
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401:
365:
338:
283:
256:
4495:"Inductive Logic Programming: Theory and methods"
3167:
3165:
2557:ILASP (Inductive Learning of Answer Set Programs)
2346:called a bridge theory satisfying the conditions
1389:and outputs the least general generalisation of
1323:, and inverse resolution, based on inverting the
896:{\displaystyle \mathrm {head} \theta \subseteq e}
4405:Bellodi, Elena; Riguzzi, Fabrizio (2014-01-15).
2820:probabilistic logic programs by considering the
557:that is inconsistent with the negative examples
3538:Advances in Knowledge Discovery and Data Mining
1800:Inverse resolution takes information about the
937:meaning that no negative example is a model of
518:Completeness requires any generated hypothesis
2342:. First they construct an intermediate theory
907:meaning every positive example is a model of
856:{\textstyle \mathrm {body} \theta \subseteq e}
4581:
3098:"Learning logical definitions from relations"
3024:. Vol. 2. Morgan Kaufmann. p. 1064.
2804:et al. presented an algorithm for performing
8:
4464: This article incorporates text from a
4208:Koller, Daphne; Pfeffer, Avi (August 1997).
2591:MIS (Model Inference System) by Ehud Shapiro
700:is said to be a model of the set of clauses
229:, a logical theory (commonly in the form of
4234:"Compressing probabilistic Prolog programs"
3967:Journal of Artificial Intelligence Research
3594:
3592:
3484:Journal of Artificial Intelligence Research
3200:Journal of Artificial Intelligence Research
2252:Inverse resolution was first introduced by
4741:
4614:
4588:
4574:
4566:
4363:Bellodi, Elena; Riguzzi, Fabrizio (2012),
4110:De Raedt, Luc; Kersting, Kristian (2008),
3710:Foundations of inductive logic programming
3682:Foundations of inductive logic programming
3657:Foundations of inductive logic programming
3473:
3471:
3469:
3467:
3146:Foundations of inductive logic programming
2978:Inductive inference of theories from facts
2924:Foundations of inductive logic programming
2848:, while the space of theories is searched
2310:
2306:
668:that contradicts the background knowledge
118:was the first to formalise induction in a
4652:Programming in the large and in the small
4506:
4422:
4271:Blockeel, Hendrik; Meert, Wannes (2007),
4184:
4113:Probabilistic Inductive Logic Programming
4086:
4076:
4025:
3988:
3978:
3942:
3872:
3780:Kimber, T.; Broda, K.; Russo, A. (2009).
3746:
3703:
3701:
3505:
3495:
3447:
3263:
3221:
3211:
3113:
2988:Lassez, J.-L.; Plotkin, G., eds. (1991).
2729:
2727:
2707:
2683:
2677:
2656:
2650:
2619:Probabilistic inductive logic programming
2415:
2386:
2351:
2289:
2233:
2227:
2206:
2200:
2179:
2173:
2152:
2146:
2125:
2119:
2098:
2092:
2071:
2065:
2044:
2038:
2017:
2011:
1990:
1984:
1963:
1957:
1936:
1930:
1909:
1903:
1883:
1862:
1856:
1835:
1829:
1809:
1754:
1748:
1727:
1721:
1660:
1647:
1620:
1600:
1580:
1555:
1549:
1528:
1522:
1501:
1495:
1474:
1468:
1448:
1427:
1421:
1400:
1394:
1373:
1367:
1346:
1340:
1294:
1288:
1267:
1261:
1241:
1217:
1211:
1191:
1167:
1161:
1140:
1134:
1097:
1084:
1072:
1051:
1038:
1026:
1001:
988:
976:
942:
912:
870:
868:
830:
828:
802:
773:
756:
754:
734:
705:
641:
614:
608:
568:
562:
535:
529:
498:
497:
484:
461:
451:
424:
420:
418:
394:
357:
351:
330:
324:
275:
269:
248:
242:
4411:Theory and Practice of Logic Programming
3733:Ray, O.; Broda, K.; Russo, A.M. (2003).
3630:Automatic Methods of Inductive Inference
2950:Automatic Methods of Inductive Inference
2645:a set of positive and negative examples
2542:FastLAS (Fast Learning from Answer Sets)
2475:And example of a Prolog-based system is
1682:first-order syntactical anti-unification
4162:
4160:
4158:
4156:
4154:
4152:
4150:
4148:
4146:
3567:"Logical settings for concept-learning"
3295:DΕΎeroski, SaΕ‘o (2001), DΕΎeroski, SaΕ‘o;
3174:"Efficient Induction of Logic Programs"
2903:
662:, forbids generation of any hypothesis
291:respectively. The output is given as a
2374:{\displaystyle B\land \neg E\models F}
1689:relative least general generalisations
1672:{\displaystyle (L,M)\in (C_{1},C_{2})}
682:In learning from interpretations, the
584:, both given the background knowledge
3956:
3954:
3735:"Hybrid abductive inductive learning"
3245:
3243:
3241:
3189:
3187:
3139:
3137:
3135:
3133:
2917:
2915:
2913:
2911:
2909:
2907:
2785:Structure learning was pioneered by
7:
4548:
4493:Muggleton, S.; De Raedt, L. (1994).
2627:. It can be considered as a form of
2547:FOIL (First Order Inductive Learner)
630:, does not impose a restriction on
3432:"Inductive logic programming at 30"
143:was first introduced in a paper by
3073:10.1016/B978-0-934613-64-4.50040-2
2771:expectation-maximisation algorithm
2423:
2394:
2359:
2326:
2317:
880:
877:
874:
871:
840:
837:
834:
831:
783:
780:
777:
774:
766:
763:
760:
757:
319:examples are given as finite sets
135:program that inductively inferred
25:
4516:Lavrac, N.; Dzeroski, S. (1994).
4468:work. Licensed under CC-BY 4.0 (
1952:. A W-operator takes two clauses
1017:and outputs a correct hypothesis
524:to explain all positive examples
5196:Partitioned global address space
4499:The Journal of Logic Programming
4459:
3636:(PhD). University of Edinburgh.
2956:(PhD). University of Edinburgh.
44:symbolic artificial intelligence
3344:Logical and Relational Learning
2992:. MIT Press. pp. 199β254.
2887:Statistical relational learning
2839:bottom clauses generated as in
2629:statistical relational learning
2432:{\displaystyle H\models \neg F}
2403:{\displaystyle F\models \neg H}
1615:, which are pairs of literals
162:in 1990 was based on upgrading
4020:. Springer. pp. 131β148.
3096:Quinlan, J. R. (August 1990).
2307:
1851:as input and returns a clause
1666:
1640:
1634:
1622:
770:
1:
4315:"Probabilistic Rule Learning"
3613:10.1016/s0004-3702(99)00067-3
3583:10.1016/S0004-3702(97)00041-6
3037:Algorithmic program debugging
1106:{\displaystyle B,E^{+},E^{-}}
1060:{\displaystyle B,E^{+},E^{-}}
1010:{\displaystyle B,E^{+},E^{-}}
678:Learning from interpretations
4723:Uniform Function Call Syntax
4508:10.1016/0743-1066(94)90035-3
4470:license statement/permission
4377:10.1007/978-3-642-31951-8_10
4285:10.1007/978-3-540-73847-3_16
4173:Frontiers in Robotics and AI
4036:10.1007/978-3-642-13840-9_13
3794:10.1007/978-3-642-04238-6_16
3757:10.1007/978-3-540-39917-9_21
3313:10.1007/978-3-662-04599-2_14
3015:"The model inference system"
2625:probabilistic logic programs
1331:Least general generalisation
110:Building on earlier work on
5417:Inductive logic programming
5191:Parallel programming models
5165:Concurrent constraint logic
4522:. New York: Ellis Horwood.
4369:Inductive Logic Programming
4327:10.1007/978-3-642-21295-6_9
4319:Inductive Logic Programming
4277:Inductive Logic Programming
4122:10.1007/978-3-540-78652-8_1
3180:. Springer/Ohmsha: 368β381.
2609:Warmr (now included in ACE)
2268:using the principle of the
1129:relation, where one clause
141:Inductive Logic Programming
100:natural language processing
36:Inductive logic programming
18:Inductive Logic Programming
5433:
5284:Metalinguistic abstraction
5151:Automatic mutual exclusion
3859:Yamamoto, Akihiro (1997).
3449:10.1007/s10994-021-06089-1
2481:meta-interpreter in Prolog
5156:Choreographic programming
4433:10.1017/s1471068413000689
4250:10.1007/s10994-007-5030-x
3838:10.1007/s10994-011-5250-y
3401:10.1007/s10994-013-5358-3
3361:10.1007/978-3-540-68856-3
3035:Shapiro, Ehud Y. (1983).
3013:Shapiro, Ehud Y. (1981).
2975:Shapiro, Ehud Y. (1981).
2456:Metainterpretive learning
2006:and returns thre clauses
1785:Inverse resolution is an
1236:, the result of applying
1229:{\textstyle C_{1}\theta }
1021:with respect to theories
597:", which postulates that
5206:Relativistic programming
4186:10.3389/frobt.2014.00006
4078:10.1186/1471-2105-13-162
3909:Kimber, Timothy (2012).
3252:New Generation Computing
1789:technique that involves
1156:subsumes another clause
402:{\displaystyle \models }
373:of positive and negated
307:Learning from entailment
3601:Artificial Intelligence
3571:Artificial Intelligence
3529:DΕΎeroski, SaΕ‘o (1996).
2867:Formal concept analysis
2498:ACE (A Combined Engine)
2487:List of implementations
1704:, then the negation of
1113:any correct hypothesis
5216:Structured concurrency
4601:Comparison by language
3627:Plotkin, G.D. (1970).
3565:De Raedt, Luc (1997).
3341:De Raedt, Luc (2008),
3305:Relational Data Mining
2947:Plotkin, G.D. (1970).
2892:Version space learning
2744:
2743:{\textstyle {H\cup B}}
2716:
2693:
2666:
2479:, which is based on a
2470:answer set programming
2433:
2404:
2375:
2336:
2243:
2216:
2189:
2162:
2135:
2108:
2081:
2054:
2027:
2000:
1973:
1946:
1919:
1892:
1872:
1845:
1818:
1764:
1737:
1673:
1609:
1589:
1565:
1538:
1511:
1484:
1457:
1437:
1410:
1383:
1356:
1304:
1277:
1250:
1230:
1200:
1177:
1150:
1107:
1061:
1011:
957:
927:
897:
857:
817:
791:
743:
720:
656:
624:
578:
545:
512:
403:
367:
340:
285:
258:
199:relational data mining
129:Model Inference System
32:
5181:Multitier programming
4997:Interface description
4597:Programming paradigms
3883:10.1007/3540635149_58
2882:Inductive probability
2877:Inductive programming
2862:Commonsense reasoning
2745:
2717:
2694:
2667:
2434:
2405:
2376:
2337:
2244:
2217:
2195:is the resolvent of
2190:
2163:
2136:
2109:
2082:
2055:
2028:
2001:
1974:
1947:
1920:
1893:
1873:
1846:
1819:
1765:
1738:
1674:
1610:
1590:
1566:
1539:
1512:
1485:
1458:
1443:, that is, a clause
1438:
1411:
1384:
1357:
1305:
1278:
1251:
1231:
1201:
1178:
1151:
1108:
1062:
1012:
958:
928:
898:
858:
818:
792:
744:
721:
657:
655:{\textstyle B\land H}
625:
579:
546:
513:
404:
368:
341:
286:
259:
224:background knowledge
195:automatic programming
30:
3990:10.1613/jair.1.13507
3507:10.1613/jair.1.13507
3223:10.1613/jair.1.13507
3067:. pp. 339β352.
2726:
2706:
2676:
2649:
2414:
2385:
2350:
2288:
2226:
2199:
2172:
2145:
2118:
2114:is the resolvent of
2091:
2064:
2037:
2010:
1983:
1956:
1929:
1902:
1898:is the resolvent of
1882:
1855:
1828:
1808:
1747:
1720:
1619:
1599:
1579:
1548:
1521:
1494:
1467:
1447:
1420:
1393:
1366:
1339:
1287:
1260:
1249:{\textstyle \theta }
1240:
1210:
1199:{\textstyle \theta }
1190:
1160:
1133:
1071:
1025:
975:
956:{\textstyle B\cup H}
941:
926:{\textstyle B\cup H}
911:
867:
827:
816:{\textstyle B\cup H}
801:
753:
742:{\textstyle \theta }
733:
719:{\textstyle B\cup H}
704:
640:
607:
561:
528:
417:
393:
350:
323:
268:
241:
166:learning algorithms
84:background knowledge
5321:Self-modifying code
4929:Probabilistic logic
4860:Functional reactive
4815:Expression-oriented
4769:Partial application
4472:). Text taken from
3353:2008lrl..book.....D
2872:Inductive reasoning
1795:resolution operator
1787:inductive reasoning
1697:is a finite set of
692:Herbrand structures
112:Inductive inference
42:) is a subfield of
5234:Attribute-oriented
5007:List comprehension
4952:Algebraic modeling
4765:Anonymous function
4657:Design by contract
4627:Jackson structures
4558:2014-03-26 at the
4501:. 19β20: 629β679.
4065:BMC Bioinformatics
3274:10.1007/bf03037227
3115:10.1007/bf00117105
2806:theory compression
2781:Structure Learning
2765:Parameter Learning
2740:
2712:
2692:{\textstyle E^{-}}
2689:
2665:{\textstyle E^{+}}
2662:
2570:2011-11-28 at the
2530:2019-08-15 at the
2513:2014-03-26 at the
2450:Yamamoto's example
2429:
2400:
2371:
2332:
2270:inverse entailment
2242:{\textstyle C_{3}}
2239:
2215:{\textstyle C_{2}}
2212:
2188:{\textstyle R_{2}}
2185:
2161:{\textstyle C_{2}}
2158:
2134:{\textstyle C_{1}}
2131:
2107:{\textstyle R_{1}}
2104:
2080:{\textstyle C_{3}}
2077:
2053:{\textstyle C_{2}}
2050:
2026:{\textstyle C_{1}}
2023:
1999:{\textstyle R_{2}}
1996:
1972:{\textstyle R_{1}}
1969:
1945:{\textstyle C_{2}}
1942:
1918:{\textstyle C_{1}}
1915:
1888:
1871:{\textstyle C_{2}}
1868:
1844:{\textstyle C_{1}}
1841:
1814:
1781:Inverse resolution
1763:{\textstyle C_{2}}
1760:
1736:{\textstyle C_{1}}
1733:
1669:
1605:
1585:
1564:{\textstyle C_{2}}
1561:
1537:{\textstyle C_{1}}
1534:
1510:{\textstyle C_{2}}
1507:
1483:{\textstyle C_{1}}
1480:
1453:
1436:{\textstyle C_{2}}
1433:
1409:{\textstyle C_{1}}
1406:
1382:{\textstyle C_{2}}
1379:
1355:{\textstyle C_{1}}
1352:
1303:{\textstyle C_{2}}
1300:
1276:{\textstyle C_{1}}
1273:
1246:
1226:
1196:
1176:{\textstyle C_{2}}
1173:
1149:{\textstyle C_{1}}
1146:
1103:
1057:
1007:
953:
923:
893:
853:
813:
787:
739:
716:
652:
623:{\textstyle E^{+}}
620:
577:{\textstyle E^{-}}
574:
544:{\textstyle E^{+}}
541:
508:
506:
463:Consistency:
411:logical entailment
399:
382:correct hypothesis
380:, respectively. A
366:{\textstyle E^{-}}
363:
339:{\textstyle E^{+}}
336:
284:{\textstyle E^{-}}
281:
257:{\textstyle E^{+}}
254:
149:inverse resolution
33:
5404:
5403:
5294:Program synthesis
5186:Organic computing
5122:
5121:
5027:Non-English-based
5002:Language-oriented
4780:Purely functional
4731:
4730:
4529:978-0-13-457870-5
4386:978-3-642-31950-1
4336:978-3-642-21294-9
4294:978-3-540-73846-6
4131:978-3-540-78651-1
4045:978-3-642-13840-9
3892:978-3-540-69587-5
3803:978-3-642-04238-6
3766:978-3-540-39917-9
3719:978-3-540-62927-6
3691:978-3-540-62927-6
3666:978-3-540-62927-6
3370:978-3-540-20040-6
3322:978-3-642-07604-6
3155:978-3-540-62927-6
3082:978-0-934613-64-4
2999:978-0-262-12156-9
2933:978-3-540-62927-6
2822:Bayesian networks
2444:anti-entailment.
2254:Stephen Muggleton
1283:, is a subset of
967:Approaches to ILP
501:
464:
427:
235:logic programming
145:Stephen Muggleton
80:negative examples
76:positive examples
54:" here refers to
48:logic programming
16:(Redirected from
5424:
5306:by demonstration
5211:Service-oriented
5201:Process-oriented
5176:Macroprogramming
5161:Concurrent logic
5032:Page description
5022:Natural language
4992:Grammar-oriented
4919:Nondeterministic
4908:Constraint logic
4810:Point-free style
4805:Functional logic
4742:
4713:Immutable object
4632:Block-structured
4615:
4590:
4583:
4576:
4567:
4544:
4542:
4541:
4532:. Archived from
4512:
4510:
4463:
4453:
4452:
4426:
4402:
4396:
4395:
4394:
4393:
4360:
4354:
4353:
4352:
4351:
4310:
4304:
4303:
4302:
4301:
4268:
4262:
4261:
4244:(2β3): 151β168.
4238:Machine Learning
4229:
4223:
4222:
4216:
4205:
4199:
4198:
4188:
4164:
4141:
4140:
4139:
4138:
4107:
4101:
4100:
4090:
4080:
4056:
4050:
4049:
4029:
4009:
4003:
4002:
3992:
3982:
3958:
3949:
3948:
3946:
3934:
3928:
3927:
3925:
3924:
3906:
3897:
3896:
3876:
3856:
3850:
3849:
3826:Machine Learning
3823:
3814:
3808:
3807:
3777:
3771:
3770:
3750:
3730:
3724:
3723:
3705:
3696:
3695:
3677:
3671:
3670:
3652:
3646:
3645:
3635:
3624:
3618:
3617:; here: Sect.2.1
3616:
3607:(1β2): 283β296.
3596:
3587:
3586:
3562:
3556:
3555:
3553:
3552:
3546:
3535:
3526:
3520:
3519:
3509:
3499:
3475:
3462:
3461:
3451:
3436:Machine Learning
3427:
3421:
3420:
3389:Machine Learning
3380:
3374:
3373:
3338:
3332:
3331:
3330:
3329:
3292:
3286:
3285:
3267:
3258:(3β4): 245β286.
3247:
3236:
3235:
3225:
3215:
3191:
3182:
3181:
3169:
3160:
3159:
3141:
3128:
3127:
3117:
3102:Machine Learning
3093:
3087:
3086:
3060:
3051:
3050:
3032:
3026:
3025:
3019:
3010:
3004:
3003:
2985:
2983:
2972:
2966:
2965:
2955:
2944:
2938:
2937:
2919:
2775:gradient descent
2760:
2756:
2749:
2747:
2746:
2741:
2739:
2721:
2719:
2718:
2713:
2698:
2696:
2695:
2690:
2688:
2687:
2671:
2669:
2668:
2663:
2661:
2660:
2641:
2442:
2438:
2436:
2435:
2430:
2409:
2407:
2406:
2401:
2380:
2378:
2377:
2372:
2345:
2341:
2339:
2338:
2333:
2283:
2279:
2275:
2267:
2248:
2246:
2245:
2240:
2238:
2237:
2221:
2219:
2218:
2213:
2211:
2210:
2194:
2192:
2191:
2186:
2184:
2183:
2167:
2165:
2164:
2159:
2157:
2156:
2140:
2138:
2137:
2132:
2130:
2129:
2113:
2111:
2110:
2105:
2103:
2102:
2086:
2084:
2083:
2078:
2076:
2075:
2059:
2057:
2056:
2051:
2049:
2048:
2032:
2030:
2029:
2024:
2022:
2021:
2005:
2003:
2002:
1997:
1995:
1994:
1978:
1976:
1975:
1970:
1968:
1967:
1951:
1949:
1948:
1943:
1941:
1940:
1924:
1922:
1921:
1916:
1914:
1913:
1897:
1895:
1894:
1889:
1877:
1875:
1874:
1869:
1867:
1866:
1850:
1848:
1847:
1842:
1840:
1839:
1823:
1821:
1820:
1815:
1769:
1767:
1766:
1761:
1759:
1758:
1742:
1740:
1739:
1734:
1732:
1731:
1714:
1708:
1695:
1678:
1676:
1675:
1670:
1665:
1664:
1652:
1651:
1614:
1612:
1611:
1606:
1594:
1592:
1591:
1586:
1570:
1568:
1567:
1562:
1560:
1559:
1543:
1541:
1540:
1535:
1533:
1532:
1516:
1514:
1513:
1508:
1506:
1505:
1489:
1487:
1486:
1481:
1479:
1478:
1462:
1460:
1459:
1454:
1442:
1440:
1439:
1434:
1432:
1431:
1415:
1413:
1412:
1407:
1405:
1404:
1388:
1386:
1385:
1380:
1378:
1377:
1361:
1359:
1358:
1353:
1351:
1350:
1327:inference rule.
1321:anti-unification
1314:Bottom-up search
1309:
1307:
1306:
1301:
1299:
1298:
1282:
1280:
1279:
1274:
1272:
1271:
1255:
1253:
1252:
1247:
1235:
1233:
1232:
1227:
1222:
1221:
1205:
1203:
1202:
1197:
1182:
1180:
1179:
1174:
1172:
1171:
1155:
1153:
1152:
1147:
1145:
1144:
1123:complete lattice
1116:
1112:
1110:
1109:
1104:
1102:
1101:
1089:
1088:
1066:
1064:
1063:
1058:
1056:
1055:
1043:
1042:
1020:
1016:
1014:
1013:
1008:
1006:
1005:
993:
992:
962:
960:
959:
954:
932:
930:
929:
924:
902:
900:
899:
894:
883:
862:
860:
859:
854:
843:
822:
820:
819:
814:
796:
794:
793:
788:
786:
769:
748:
746:
745:
740:
725:
723:
722:
717:
698:
672:
666:
661:
659:
658:
653:
634:
629:
627:
626:
621:
619:
618:
603:does not entail
601:
588:
583:
581:
580:
575:
573:
572:
555:
550:
548:
547:
542:
540:
539:
522:
517:
515:
514:
509:
507:
503:
502:
489:
488:
465:
462:
456:
455:
428:
425:
408:
406:
405:
400:
387:
372:
370:
369:
364:
362:
361:
345:
343:
342:
337:
335:
334:
298:
290:
288:
287:
282:
280:
279:
263:
261:
260:
255:
253:
252:
227:
158:, introduced by
21:
5432:
5431:
5427:
5426:
5425:
5423:
5422:
5421:
5407:
5406:
5405:
5400:
5342:
5335:
5226:Metaprogramming
5220:
5136:
5131:
5118:
5100:Graph rewriting
4938:
4914:Inductive logic
4894:Abductive logic
4880:
4837:
4800:Dependent types
4748:
4727:
4699:Prototype-based
4679:
4677:Object-oriented
4671:
4667:Nested function
4662:Invariant-based
4604:
4594:
4564:
4560:Wayback Machine
4539:
4537:
4530:
4515:
4492:
4488:
4486:Further reading
4480:Frontiers Media
4457:
4456:
4404:
4403:
4399:
4391:
4389:
4387:
4362:
4361:
4357:
4349:
4347:
4337:
4312:
4311:
4307:
4299:
4297:
4295:
4270:
4269:
4265:
4231:
4230:
4226:
4214:
4207:
4206:
4202:
4166:
4165:
4144:
4136:
4134:
4132:
4109:
4108:
4104:
4058:
4057:
4053:
4046:
4027:10.1.1.297.7992
4011:
4010:
4006:
3960:
3959:
3952:
3936:
3935:
3931:
3922:
3920:
3908:
3907:
3900:
3893:
3858:
3857:
3853:
3821:
3816:
3815:
3811:
3804:
3779:
3778:
3774:
3767:
3748:10.1.1.212.6602
3732:
3731:
3727:
3720:
3707:
3706:
3699:
3692:
3679:
3678:
3674:
3667:
3654:
3653:
3649:
3633:
3626:
3625:
3621:
3598:
3597:
3590:
3564:
3563:
3559:
3550:
3548:
3544:
3533:
3528:
3527:
3523:
3477:
3476:
3465:
3429:
3428:
3424:
3382:
3381:
3377:
3371:
3340:
3339:
3335:
3327:
3325:
3323:
3294:
3293:
3289:
3249:
3248:
3239:
3193:
3192:
3185:
3171:
3170:
3163:
3156:
3143:
3142:
3131:
3095:
3094:
3090:
3083:
3062:
3061:
3054:
3047:
3034:
3033:
3029:
3017:
3012:
3011:
3007:
3000:
2987:
2981:
2974:
2973:
2969:
2953:
2946:
2945:
2941:
2934:
2921:
2920:
2905:
2900:
2858:
2795:graphical model
2783:
2767:
2758:
2754:
2724:
2723:
2704:
2703:
2679:
2674:
2673:
2652:
2647:
2646:
2639:
2621:
2572:Wayback Machine
2532:Wayback Machine
2515:Wayback Machine
2489:
2458:
2440:
2412:
2411:
2383:
2382:
2348:
2347:
2343:
2286:
2285:
2281:
2277:
2273:
2265:
2262:
2260:Top-down search
2229:
2224:
2223:
2202:
2197:
2196:
2175:
2170:
2169:
2148:
2143:
2142:
2121:
2116:
2115:
2094:
2089:
2088:
2067:
2062:
2061:
2040:
2035:
2034:
2013:
2008:
2007:
1986:
1981:
1980:
1959:
1954:
1953:
1932:
1927:
1926:
1905:
1900:
1899:
1880:
1879:
1858:
1853:
1852:
1831:
1826:
1825:
1806:
1805:
1783:
1750:
1745:
1744:
1723:
1718:
1717:
1712:
1706:
1693:
1656:
1643:
1617:
1616:
1597:
1596:
1577:
1576:
1551:
1546:
1545:
1524:
1519:
1518:
1497:
1492:
1491:
1470:
1465:
1464:
1463:that subsumes
1445:
1444:
1423:
1418:
1417:
1396:
1391:
1390:
1369:
1364:
1363:
1342:
1337:
1336:
1333:
1316:
1290:
1285:
1284:
1263:
1258:
1257:
1238:
1237:
1213:
1208:
1207:
1188:
1187:
1163:
1158:
1157:
1136:
1131:
1130:
1114:
1093:
1080:
1069:
1068:
1047:
1034:
1023:
1022:
1018:
997:
984:
973:
972:
969:
939:
938:
909:
908:
865:
864:
825:
824:
799:
798:
751:
750:
749:and any clause
731:
730:
702:
701:
696:
680:
670:
664:
638:
637:
632:
610:
605:
604:
599:
586:
564:
559:
558:
553:
531:
526:
525:
520:
505:
504:
495:
490:
480:
466:
458:
457:
447:
445:
440:
429:
415:
414:
391:
390:
385:
353:
348:
347:
326:
321:
320:
309:
296:
271:
266:
265:
244:
239:
238:
225:
216:
108:
23:
22:
15:
12:
11:
5:
5430:
5428:
5420:
5419:
5409:
5408:
5402:
5401:
5399:
5398:
5393:
5388:
5383:
5378:
5373:
5368:
5363:
5358:
5353:
5347:
5345:
5337:
5336:
5334:
5333:
5328:
5323:
5318:
5313:
5291:
5286:
5281:
5271:
5266:
5261:
5256:
5251:
5246:
5236:
5230:
5228:
5222:
5221:
5219:
5218:
5213:
5208:
5203:
5198:
5193:
5188:
5183:
5178:
5173:
5168:
5158:
5153:
5148:
5142:
5140:
5124:
5123:
5120:
5119:
5117:
5116:
5111:
5096:Transformation
5093:
5088:
5083:
5078:
5073:
5068:
5063:
5058:
5053:
5048:
5043:
5034:
5029:
5024:
5019:
5014:
5009:
5004:
4999:
4994:
4989:
4984:
4982:Differentiable
4979:
4969:
4962:Automata-based
4959:
4954:
4948:
4946:
4940:
4939:
4937:
4936:
4931:
4926:
4921:
4916:
4911:
4901:
4896:
4890:
4888:
4882:
4881:
4879:
4878:
4873:
4868:
4863:
4853:
4847:
4845:
4839:
4838:
4836:
4835:
4829:Function-level
4826:
4817:
4812:
4807:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4762:
4756:
4754:
4739:
4733:
4732:
4729:
4728:
4726:
4725:
4720:
4715:
4710:
4705:
4691:
4689:
4673:
4672:
4670:
4669:
4664:
4659:
4654:
4649:
4644:
4642:Non-structured
4639:
4634:
4629:
4623:
4621:
4612:
4606:
4605:
4595:
4593:
4592:
4585:
4578:
4570:
4563:
4562:
4545:
4528:
4513:
4489:
4487:
4484:
4455:
4454:
4417:(2): 169β212.
4397:
4385:
4355:
4335:
4305:
4293:
4263:
4224:
4200:
4142:
4130:
4102:
4051:
4044:
4004:
3950:
3929:
3898:
3891:
3874:10.1.1.54.2975
3851:
3809:
3802:
3772:
3765:
3725:
3718:
3697:
3690:
3672:
3665:
3647:
3619:
3588:
3577:(1): 187β201.
3557:
3521:
3463:
3442:(1): 147β172.
3422:
3375:
3369:
3333:
3321:
3287:
3265:10.1.1.31.1630
3237:
3183:
3161:
3154:
3129:
3108:(3): 239β266.
3088:
3081:
3052:
3045:
3027:
3005:
2998:
2967:
2939:
2932:
2902:
2901:
2899:
2896:
2895:
2894:
2889:
2884:
2879:
2874:
2869:
2864:
2857:
2854:
2782:
2779:
2766:
2763:
2738:
2735:
2732:
2715:{\textstyle H}
2711:
2700:
2699:
2686:
2682:
2659:
2655:
2643:
2620:
2617:
2616:
2615:
2610:
2607:
2602:
2597:
2592:
2589:
2584:
2579:
2574:
2562:
2559:
2554:
2549:
2544:
2539:
2534:
2522:
2517:
2505:
2500:
2495:
2488:
2485:
2457:
2454:
2428:
2425:
2422:
2419:
2399:
2396:
2393:
2390:
2370:
2367:
2364:
2361:
2358:
2355:
2331:
2328:
2325:
2322:
2319:
2316:
2313:
2309:
2305:
2302:
2299:
2296:
2293:
2261:
2258:
2236:
2232:
2209:
2205:
2182:
2178:
2155:
2151:
2128:
2124:
2101:
2097:
2074:
2070:
2047:
2043:
2020:
2016:
1993:
1989:
1966:
1962:
1939:
1935:
1912:
1908:
1891:{\textstyle R}
1887:
1865:
1861:
1838:
1834:
1817:{\textstyle R}
1813:
1782:
1779:
1757:
1753:
1730:
1726:
1668:
1663:
1659:
1655:
1650:
1646:
1642:
1639:
1636:
1633:
1630:
1627:
1624:
1608:{\textstyle D}
1604:
1588:{\textstyle C}
1584:
1558:
1554:
1531:
1527:
1504:
1500:
1477:
1473:
1456:{\textstyle C}
1452:
1430:
1426:
1403:
1399:
1376:
1372:
1349:
1345:
1332:
1329:
1315:
1312:
1297:
1293:
1270:
1266:
1245:
1225:
1220:
1216:
1195:
1183:if there is a
1170:
1166:
1143:
1139:
1100:
1096:
1092:
1087:
1083:
1079:
1076:
1054:
1050:
1046:
1041:
1037:
1033:
1030:
1004:
1000:
996:
991:
987:
983:
980:
968:
965:
952:
949:
946:
922:
919:
916:
892:
889:
886:
882:
879:
876:
873:
852:
849:
846:
842:
839:
836:
833:
812:
809:
806:
785:
782:
779:
776:
772:
768:
765:
762:
759:
738:
715:
712:
709:
679:
676:
651:
648:
645:
617:
613:
571:
567:
538:
534:
496:
494:
491:
487:
483:
479:
476:
473:
470:
467:
460:
459:
454:
450:
446:
444:
441:
439:
436:
433:
430:
423:
422:
398:
360:
356:
333:
329:
308:
305:
278:
274:
251:
247:
215:
212:
191:bioinformatics
116:Gordon Plotkin
107:
104:
96:bioinformatics
92:
91:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5429:
5418:
5415:
5414:
5412:
5397:
5394:
5392:
5389:
5387:
5384:
5382:
5379:
5377:
5374:
5372:
5369:
5367:
5366:Data-oriented
5364:
5362:
5359:
5357:
5354:
5352:
5349:
5348:
5346:
5344:
5338:
5332:
5329:
5327:
5324:
5322:
5319:
5317:
5314:
5311:
5307:
5303:
5299:
5295:
5292:
5290:
5287:
5285:
5282:
5279:
5275:
5272:
5270:
5267:
5265:
5264:Homoiconicity
5262:
5260:
5257:
5255:
5252:
5250:
5247:
5244:
5240:
5237:
5235:
5232:
5231:
5229:
5227:
5223:
5217:
5214:
5212:
5209:
5207:
5204:
5202:
5199:
5197:
5194:
5192:
5189:
5187:
5184:
5182:
5179:
5177:
5174:
5172:
5171:Concurrent OO
5169:
5166:
5162:
5159:
5157:
5154:
5152:
5149:
5147:
5144:
5143:
5141:
5139:
5134:
5129:
5125:
5115:
5112:
5109:
5105:
5101:
5097:
5094:
5092:
5089:
5087:
5084:
5082:
5079:
5077:
5074:
5072:
5069:
5067:
5066:Set-theoretic
5064:
5062:
5059:
5057:
5054:
5052:
5049:
5047:
5046:Probabilistic
5044:
5042:
5038:
5035:
5033:
5030:
5028:
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5003:
5000:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4977:
4973:
4970:
4967:
4963:
4960:
4958:
4955:
4953:
4950:
4949:
4947:
4945:
4941:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4912:
4909:
4905:
4902:
4900:
4897:
4895:
4892:
4891:
4889:
4887:
4883:
4877:
4874:
4872:
4869:
4867:
4864:
4861:
4857:
4854:
4852:
4849:
4848:
4846:
4844:
4840:
4834:
4830:
4827:
4825:
4824:Concatenative
4821:
4818:
4816:
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4770:
4766:
4763:
4761:
4758:
4757:
4755:
4752:
4747:
4743:
4740:
4738:
4734:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4700:
4696:
4693:
4692:
4690:
4687:
4683:
4678:
4674:
4668:
4665:
4663:
4660:
4658:
4655:
4653:
4650:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4624:
4622:
4620:
4616:
4613:
4611:
4607:
4602:
4598:
4591:
4586:
4584:
4579:
4577:
4572:
4571:
4568:
4561:
4557:
4554:
4550:
4546:
4536:on 2004-09-06
4535:
4531:
4525:
4521:
4520:
4514:
4509:
4504:
4500:
4496:
4491:
4490:
4485:
4483:
4481:
4477:
4476:
4471:
4467:
4462:
4450:
4446:
4442:
4438:
4434:
4430:
4425:
4420:
4416:
4412:
4408:
4401:
4398:
4388:
4382:
4378:
4374:
4370:
4366:
4359:
4356:
4346:
4342:
4338:
4332:
4328:
4324:
4320:
4316:
4309:
4306:
4296:
4290:
4286:
4282:
4278:
4274:
4267:
4264:
4259:
4255:
4251:
4247:
4243:
4239:
4235:
4228:
4225:
4220:
4213:
4212:
4204:
4201:
4196:
4192:
4187:
4182:
4178:
4174:
4170:
4163:
4161:
4159:
4157:
4155:
4153:
4151:
4149:
4147:
4143:
4133:
4127:
4123:
4119:
4115:
4114:
4106:
4103:
4098:
4094:
4089:
4084:
4079:
4074:
4070:
4066:
4062:
4055:
4052:
4047:
4041:
4037:
4033:
4028:
4023:
4019:
4015:
4008:
4005:
4000:
3996:
3991:
3986:
3981:
3976:
3972:
3968:
3964:
3957:
3955:
3951:
3945:
3940:
3933:
3930:
3919:on 2022-10-21
3918:
3914:
3913:
3905:
3903:
3899:
3894:
3888:
3884:
3880:
3875:
3870:
3866:
3862:
3855:
3852:
3847:
3843:
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3547:on 2021-09-27
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3046:0-262-19218-7
3042:
3039:. MIT Press.
3038:
3031:
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3016:
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2986:Reprinted in
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2787:Daphne Koller
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2272:for theories
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164:propositional
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5371:Event-driven
4913:
4775:Higher-order
4703:Object-based
4538:. Retrieved
4534:the original
4518:
4498:
4474:
4466:free content
4458:
4414:
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4266:
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3921:. Retrieved
3917:the original
3911:
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3537:
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3297:LavraΔ, Nada
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292:
223:
217:
203:
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160:Ross Quinlan
153:
140:
124:Ehud Shapiro
109:
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79:
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60:mathematical
51:
39:
35:
34:
5381:Intentional
5361:Data-driven
5343:of concerns
5302:Inferential
5289:Multi-stage
5269:Interactive
5146:Actor-based
5133:distributed
5076:Stack-based
4876:Synchronous
4833:Value-level
4820:Applicative
4737:Declarative
4695:Class-based
4549:Atom system
3832:: 115β139.
3490:: 779β782.
2846:beam search
2791:first-order
1127:subsumption
935:consistent,
726:if for any
409:stands for
137:Horn clause
131:in 1981: a
46:which uses
5356:Components
5341:Separation
5316:Reflective
5310:by example
5254:Extensible
5128:Concurrent
5104:Production
5091:Templating
5071:Simulation
5056:Scientific
4976:Spacecraft
4904:Constraint
4899:Answer set
4851:Flow-based
4751:comparison
4746:Functional
4718:Persistent
4682:comparison
4647:Procedural
4619:Structured
4610:Imperative
4540:2004-09-22
4392:2023-12-09
4350:2023-12-09
4300:2023-12-09
4137:2023-12-09
3980:2008.07912
3923:2022-10-21
3551:2021-09-27
3497:2008.07912
3328:2023-11-27
3213:2008.07912
2898:References
2525:DL-Learner
2462:meta-level
2410:. Then as
2087:such that
1878:such that
1716:with both
1573:selections
1325:resolution
1206:such that
1125:under the
823:such that
293:hypothesis
220:entailment
88:hypothesis
5243:Inductive
5239:Automatic
5061:Scripting
4760:Recursive
4441:1471-0684
4424:1309.2080
4258:0885-6125
4195:2296-9144
4022:CiteSeerX
3999:1076-9757
3944:1407.3836
3869:CiteSeerX
3743:CiteSeerX
3642:1842/6656
3516:1076-9757
3458:0885-6125
3417:254738603
3409:0885-6125
3260:CiteSeerX
3232:1076-9757
3124:0885-6125
2962:1842/6656
2800:In 2008,
2734:∪
2685:−
2424:¬
2421:⊨
2395:¬
2392:⊨
2366:⊨
2360:¬
2357:∧
2327:¬
2324:⊨
2318:¬
2315:∧
2308:⟺
2301:⊨
2295:∧
1802:resolvent
1791:inverting
1638:∈
1244:θ
1224:θ
1194:θ
1099:−
1053:−
1003:−
948:∪
918:∪
905:complete,
888:⊆
885:θ
848:⊆
845:θ
808:∪
771:←
737:θ
711:∪
647:∧
595:Necessity
570:−
486:−
478:∪
472:∪
443:⊨
435:∪
397:⊨
359:−
277:−
151:in 1988.
52:inductive
5411:Category
5396:Subjects
5386:Literate
5376:Features
5331:Template
5326:Symbolic
5298:Bayesian
5278:Hygienic
5138:parallel
5017:Modeling
5012:Low-code
4987:End-user
4924:Ontology
4856:Reactive
4843:Dataflow
4556:Archived
4449:17669522
4345:11727522
4097:22783946
3846:11347607
3299:(eds.),
3282:12643399
2856:See also
2850:greedily
2802:De Raedt
2613:ProGolem
2568:Archived
2528:Archived
2520:Claudien
2511:Archived
1702:literals
688:negative
684:positive
493:⊭
378:literals
317:negative
313:positive
233:used in
74:Schema:
64:database
5351:Aspects
5259:Generic
5249:Dynamic
5108:Pattern
5086:Tactile
5051:Quantum
5041:filters
4972:Command
4871:Streams
4866:Signals
4637:Modular
4088:3458898
4071:: 162.
3973:: 795.
3349:Bibcode
3206:: 808.
2833:ProbLog
2810:ProbLog
2582:Metagol
2477:Metagol
231:clauses
214:Setting
207:Metagol
120:clausal
106:History
68:entails
5114:Visual
5081:System
4966:Action
4790:Strict
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2818:ground
2773:or by
2634:Given
2600:PROGOL
2595:Popper
2561:Imparo
2466:Prolog
1699:ground
933:, and
375:ground
180:Progol
133:Prolog
5391:Roles
5274:Macro
5037:Pipes
4957:Array
4934:Query
4886:Logic
4795:GADTs
4785:Total
4708:Agent
4445:S2CID
4419:arXiv
4341:S2CID
4219:IJCAI
4215:(PDF)
3975:arXiv
3939:arXiv
3842:S2CID
3822:(PDF)
3634:(PDF)
3545:(PDF)
3534:(PDF)
3492:arXiv
3413:S2CID
3278:S2CID
3208:arXiv
3018:(PDF)
2982:(PDF)
2954:(PDF)
2831:with
2642:, and
2552:Golem
2503:Aleph
1925:and
1775:Golem
1575:from
500:false
184:Aleph
176:Golem
5039:and
4686:list
4524:ISBN
4482:.
4437:ISSN
4381:ISBN
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4093:PMID
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3077:ISBN
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2994:ISBN
2928:ISBN
2829:FOIL
2672:and
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2468:and
2381:and
2222:and
2168:and
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1979:and
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2100:1
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2073:3
2069:C
2046:2
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2019:1
2015:C
1992:2
1988:R
1965:1
1961:R
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1934:C
1911:1
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1886:R
1864:2
1860:C
1837:1
1833:C
1812:R
1756:2
1752:C
1729:1
1725:C
1713:B
1707:B
1694:B
1667:)
1662:2
1658:C
1654:,
1649:1
1645:C
1641:(
1635:)
1632:M
1629:,
1626:L
1623:(
1603:D
1583:C
1557:2
1553:C
1530:1
1526:C
1503:2
1499:C
1476:1
1472:C
1451:C
1429:2
1425:C
1402:1
1398:C
1375:2
1371:C
1348:1
1344:C
1296:2
1292:C
1269:1
1265:C
1219:1
1215:C
1169:2
1165:C
1142:1
1138:C
1115:H
1095:E
1091:,
1086:+
1082:E
1078:,
1075:B
1049:E
1045:,
1040:+
1036:E
1032:,
1029:B
1019:H
999:E
995:,
990:+
986:E
982:,
979:B
951:H
945:B
921:H
915:B
891:e
881:d
878:a
875:e
872:h
851:e
841:y
838:d
835:o
832:b
811:H
805:B
784:y
781:d
778:o
775:b
767:d
764:a
761:e
758:h
714:H
708:B
697:e
671:B
665:h
650:H
644:B
633:h
616:+
612:E
600:B
587:B
566:E
554:h
537:+
533:E
521:h
482:E
475:H
469:B
453:+
449:E
438:H
432:B
386:H
355:E
332:+
328:E
297:H
273:E
250:+
246:E
226:B
90:.
38:(
20:)
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